Slip Effect Study of 4:1 Contraction Flow for Oldroyd-B Model
The numerical simulation of the slip effect via
vicoelastic fluid for 4:1 contraction problem is investigated with
regard to kinematic behaviors of streamlines and stress tensor by
models of the Navier-Stokes and Oldroyd-B equations. Twodimensional
spatial reference system of incompressible creeping flow
with and without slip velocity is determined and the finite element
method of a semi-implicit Taylor-Galerkin pressure-correction is
applied to compute the problem of this Cartesian coordinate system
including the schemes of velocity gradient recovery method and the
streamline-Upwind / Petrov-Galerkin procedure. The slip effect at
channel wall is added to calculate after each time step in order to
intend the alteration of flow path. The result of stress values and the
vortices are reduced by the optimum slip coefficient of 0.1 with near
the outcome of analytical solution.
<p>[1] K. Walters, D. M. Rawlinson , On some contraction flows for Boger
fluid, Rheol. Acta., vol 21, pp. 547-552, 1982.
[2] D.V. Boger, Viscoelastic flows through contractions , Ann. Rev. Fluid
Mech., vol 19, pp. 157–182, 1987.
[3] T.N. Phillips, A.J. Williams, Viscoelastic flow through a planar
contraction using a semi-Lagrangian finite volume method, J. Non-
Newtonian Fluid Mech., vol 87, pp. 215–246, 1999.
[4] T.N. Phillips, A.J. Williams, Comparison of creeping and inertial
flow of an Oldroyd B fluid through planar and axisymmetric
contractions, J. Non-Newtonian Fluid Mech., vol 108, pp. 25–47,
2002.
[5] M. Aboubacar and M.F. Webster, “A cell-vertex finite volume/element
method on triangles for abrupt contraction viscoelastic flows”, J. Non-
Newtonian Fluid Mech., vol 98, pp. 83–106, 2001.
[6] M. Aboubacar, H. Matallah, M.F. Webster, Highly elastic solutions for
Oldroyd-B and Phan-Thien/Tanner fluids with a finite volume/element
method : planar contraction flows, J. Non-Newtonian Fluid Mech., vol
103, pp. 65–103, 2002.
[7] M.A. Alves, D. Torres, M.P. Goncalves, P.J. Oliverira, F.T. Pinho, On
the effect of contraction ratio in viscoelastic flow through abrupt
contractions, J. Non-Newtonian Fluid Mech., vol 122, pp. 117–130,
2004.
[8] V. Ngamaramvaranggul, M. F. Webster, Viscoelastic simulation of
stick-slip and die-swell flows, Int. J. Num. Meth. Fluids., vol 36, pp.
539-595, 2001.
[9] V. Ngamaramvaranggul and M. F. Webster, Simulation of pressuretooling
wire-coating flows with Phan-Thien/Tanner models Int. J. Num.
Meth. Fluids, vol 38, pp. 677-710, 2002.
[10] W. J. Silliman, L. E. Scriven, Separating flow near a static contact line :
Slip at a wall and shape of a free surface, J. Comp. Phys., vol 34, pp.
287-313, 1980.
[11] A. V. Ramamurthy, Wall slip in viscous fluids and influence of
materials of construction, J. Rheol., vol 30, pp. 337-357, 1986.
[12] T. Q. Jiang, A. C. Young, A. B. Metzner, The rheological
characterization of HPG gels: Measurement of slip velocity in capillary
tubes, Rheol. Acta, vol 25 no.4 , pp. 397-404, 1986.
[13] N. Phan-Thien, Influence of wall slip on extrudate swell : a boundary
element investigation, J. Non-Newtonian Fluid Mech., vol 26, pp. 327-
340, 1988.
[14] V. Ngamaramvaranggul, M. F. Webster, Simulation of coating flows
with slip effects, Int. J. Num. Meth. Fluids., vol 33, pp. 961-992,2000.
[15] M.W. Johnson, D. Segalman, A model for viscoelastic fluid behavior
which allows non-affine deformation, J. Non-Newtonian Fluid Mech.,
vol 2 pp. 255-270, 1977.</p>
<p>[1] K. Walters, D. M. Rawlinson , On some contraction flows for Boger
fluid, Rheol. Acta., vol 21, pp. 547-552, 1982.
[2] D.V. Boger, Viscoelastic flows through contractions , Ann. Rev. Fluid
Mech., vol 19, pp. 157–182, 1987.
[3] T.N. Phillips, A.J. Williams, Viscoelastic flow through a planar
contraction using a semi-Lagrangian finite volume method, J. Non-
Newtonian Fluid Mech., vol 87, pp. 215–246, 1999.
[4] T.N. Phillips, A.J. Williams, Comparison of creeping and inertial
flow of an Oldroyd B fluid through planar and axisymmetric
contractions, J. Non-Newtonian Fluid Mech., vol 108, pp. 25–47,
2002.
[5] M. Aboubacar and M.F. Webster, “A cell-vertex finite volume/element
method on triangles for abrupt contraction viscoelastic flows”, J. Non-
Newtonian Fluid Mech., vol 98, pp. 83–106, 2001.
[6] M. Aboubacar, H. Matallah, M.F. Webster, Highly elastic solutions for
Oldroyd-B and Phan-Thien/Tanner fluids with a finite volume/element
method : planar contraction flows, J. Non-Newtonian Fluid Mech., vol
103, pp. 65–103, 2002.
[7] M.A. Alves, D. Torres, M.P. Goncalves, P.J. Oliverira, F.T. Pinho, On
the effect of contraction ratio in viscoelastic flow through abrupt
contractions, J. Non-Newtonian Fluid Mech., vol 122, pp. 117–130,
2004.
[8] V. Ngamaramvaranggul, M. F. Webster, Viscoelastic simulation of
stick-slip and die-swell flows, Int. J. Num. Meth. Fluids., vol 36, pp.
539-595, 2001.
[9] V. Ngamaramvaranggul and M. F. Webster, Simulation of pressuretooling
wire-coating flows with Phan-Thien/Tanner models Int. J. Num.
Meth. Fluids, vol 38, pp. 677-710, 2002.
[10] W. J. Silliman, L. E. Scriven, Separating flow near a static contact line :
Slip at a wall and shape of a free surface, J. Comp. Phys., vol 34, pp.
287-313, 1980.
[11] A. V. Ramamurthy, Wall slip in viscous fluids and influence of
materials of construction, J. Rheol., vol 30, pp. 337-357, 1986.
[12] T. Q. Jiang, A. C. Young, A. B. Metzner, The rheological
characterization of HPG gels: Measurement of slip velocity in capillary
tubes, Rheol. Acta, vol 25 no.4 , pp. 397-404, 1986.
[13] N. Phan-Thien, Influence of wall slip on extrudate swell : a boundary
element investigation, J. Non-Newtonian Fluid Mech., vol 26, pp. 327-
340, 1988.
[14] V. Ngamaramvaranggul, M. F. Webster, Simulation of coating flows
with slip effects, Int. J. Num. Meth. Fluids., vol 33, pp. 961-992,2000.
[15] M.W. Johnson, D. Segalman, A model for viscoelastic fluid behavior
which allows non-affine deformation, J. Non-Newtonian Fluid Mech.,
vol 2 pp. 255-270, 1977.</p>
@article{"International Journal of Engineering, Mathematical and Physical Sciences:54538", author = "N. Thongjub and B. Puangkird and V. Ngamaramvaranggul", title = "Slip Effect Study of 4:1 Contraction Flow for Oldroyd-B Model", abstract = "The numerical simulation of the slip effect via
vicoelastic fluid for 4:1 contraction problem is investigated with
regard to kinematic behaviors of streamlines and stress tensor by
models of the Navier-Stokes and Oldroyd-B equations. Twodimensional
spatial reference system of incompressible creeping flow
with and without slip velocity is determined and the finite element
method of a semi-implicit Taylor-Galerkin pressure-correction is
applied to compute the problem of this Cartesian coordinate system
including the schemes of velocity gradient recovery method and the
streamline-Upwind / Petrov-Galerkin procedure. The slip effect at
channel wall is added to calculate after each time step in order to
intend the alteration of flow path. The result of stress values and the
vortices are reduced by the optimum slip coefficient of 0.1 with near
the outcome of analytical solution.
", keywords = "Slip effect, Oldroyd-B fluid, slip coefficient, time
stepping method.", volume = "7", number = "8", pages = "1286-8", }
